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Duals of algebraic matroids need not be algebraic
Matt Larson, Tuong Le
Source abstract
We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It is obtained by gluing an algebraic realization of the non-Fano matroid to a realization of the Fano matroid. Its dual is shown not to be algebraic using the Ingleton-Main lemma.
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